"Heat Equation Derivative Formulas for Vector Bundles," by B. Driver
and Anton Thalmaier.
(UCSD and Univ. of Bonn Preprint, March 2000, and 1998 )
Available as a DVI
file (284K) or a PDF file (769K).
Abstract
We use martingale methods to give Bismut type derivative formulas
for differentials and codifferentials of heat semigroups on forms, and more
generally for sections of vector bundles. The formulas are mainly in terms
of Weitzenb\"{o}ck curvature terms, in most cases derivatives of the
curvature are not involved. In particular, our results improve the formula
in Driver \cite{Driver:97b} for logarithmic derivatives of the heat kernel
measure on a Riemannian manifold. Our formulas also include the formulas in
Elworthy and Li \cite{ElworthyLi:98}.
March 2000
